Question

I would like to know the math behind the answer to A and B, I have tried several routes and cannot get it right. Thanks in advance.

Constants Periodic Table A block of inertia m sits on a smooth surface (Figure 1). A light string is attached to it and placed over a solid pulley of inertia 7 m and radius R, and a ball of inertia m is attached to the free end of the string. Part A If there is no slippage between string and pulley, determine the magnitude of the block's acceleration. Express your answer to two significant digits and include the appropriate units. HA ? Value Submit Previous Answers Request Answer Part B If you detach the ball and pull down on the hanging string with a force of magnitude mg, what is the magnitude of the block's acceleration? Express your answer to two significant digits and include the appropriate units. μΑ ? Figure 1 of 1 Value Units Submit Request Answer m Provide Feedback Next > m Pearson

Answer 1

Part A Free body diagram of block ball and pulley system 7m from Newton's law, for motion of block Fnet = ma T2 = ma from Newton's law, for motion of ball mg - Ti = ma T1 = m(g-a) For rotational motion of pulley iner la TR - TTR = la TR - TR = 7mR2 2 a For rolling without slipping a = R

7mR2 TR - TTR = 2 R T1-T2 = 3.5ma míg - a) - ma = 3.5ma mg - 2ma = 3.5ma a= 5.5 9.81 5.5 a a = 1.8 x m/s2 Part B Free body diagram of blocks and pulley when a force mg is applied 7m a va Fring from Newton's law, for motion of block = ma Fnet T, = ma For rotational motion of pulley Ther = la FR-T2R = la

mgR - T2R = 7mR2 a 2 For rolling without slipping a = 7mR2 a mgR - TAR Х 2 R mg - T2 = 3.5ma mg - ma = 3.5mg a = g 4.5 9.81 a = 4.5 a = 2.2 x m/s2